A new grey prediction model FGM(1, 1)

The effectiveness of the first entry of the original series by GM(1, 1) is researched in this paper. The results show that the modelling values and forecasts are independent of the first entry of the original series. The grey prediction model presented in this paper is called first-entry GM(1, 1), a...

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Vydáno v:Mathematical and computer modelling Ročník 49; číslo 7; s. 1416 - 1426
Hlavní autor: Tien, Tzu-Li
Médium: Journal Article
Jazyk:angličtina
Vydáno: Kidlington Elsevier Ltd 01.04.2009
Elsevier
Témata:
AGO
Determinant
Effectiveness
Exact sciences and technology
FGM(1, 1)
Geometry
GM(1, 1)
Grey prediction
Mathematical analysis
Mathematics
Methods of scientific computing (including symbolic computation, algebraic computation)
Numerical analysis. Scientific computation
Sciences and techniques of general use
AGO
FGM(1, 1)
Effectiveness
Grey prediction
Determinant
GM(1, 1)
Grey prediction; GM1
Scientific computation
Applied mathematics
1; FGM1
1; AGO; Effectiveness; Determinant
Mathematical model
Algorithm
Computer aided analysis
ISSN:0895-7177, 1872-9479
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Popis
Shrnutí:The effectiveness of the first entry of the original series by GM(1, 1) is researched in this paper. The results show that the modelling values and forecasts are independent of the first entry of the original series. The grey prediction model presented in this paper is called first-entry GM(1, 1), abbreviated as FGM(1, 1), which is based on the existing GM(1, 1) but modelled with data including the first-entry’s messages of the original series. A proof concerning this subject has been presented by other authors. However, the algorithm of their direct proof is too complicated. A more compact algorithm is presented in this paper to prove the first entry of the original series ineffective to the modelling values and forecasts by GM(1, 1). Then, an arbitrary number can be inserted in the front of the original series to extract the messages from its first entry. Only a few data (usually fewer than ten) are used for model building. This paper deals with the effectiveness of the first entry of the original series by GM(1, 1).
ISSN:0895-7177
1872-9479
DOI:10.1016/j.mcm.2008.11.015